I have a degree in mathematics, and I've worked as a statistician and done some programming work. I'm very strong in my math/stats/programming background and have browsed some QF books, and I'm very interested. I'm American, but I'm currently out of the country, and I don't know if seeking a hedge fund/firm where I am is so practical.

Do I need a fat bank roll to get started, or are there fields of finance that I can perhaps get involved with assuming I put in the time to study and (hopefully) develop killer software.

4 Answers
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At the top of this list I still recommend you to seek employment in order to learn from others in QF space. Could you possible work in a quant team within an investment bank where you currently reside?

Start to reach out to the quant finance community so you are connected once you decide to locate to where you can practice this discipline.reach out to alumni, friends, anyone who may work in this field.

have you considered an academic career in quantitative finance?

Spend sufficient time in figuring out which part of quant finance you really like: Risk management, time series modeling, high frequency trading, proprietary trading, discretionary trading, fundamental quantitative research...

make sure you are on top of the latest developments at the R front and know which packages are utilized. Refresh your skills in the mathematical and statistical modeling aspects. Are you familiar with new C++ libraries such as AMP, .net 4.0 or 4.5, you can use Python? Those are just examples but knowing well the tools of the trade is a basic requirement.

You then could proceed to start reading books which may help you to better understand what quants really do. I like "my life as a quant" by Derman but personally I think nothing beats direct contact with alumni who work in the industry. Also get your hands on "quantitative Finance interview questions" ( I think that was the title but not 100% sure, but I am sure it's by falcon crack)

How about you start profiling and modeling financial time series? This will sharpen your skills to analyze potential strategy opportunities as well as force you to use the tools you would be expected to know.

you could develop a trading architecture (or extend existing open source ones) to demonstrate to others later on that you indeed have a passion for this field and want to work there. Does not have to be a trading architecture if you find tools that let you test strategy ideas then I think nothing beats approaching employers in the future with strategies in your hand that could be profitably employed.

Edit: Freddy's answer is good -- we wrote concurrently. He rightly points out that QF is a broad field, and that it is among other things a community. Here, I describe a practical, down-to-earth path for getting your feet wet in one key piece of it -- software and model development for derivatives analysis, starting with vanilla options. Your best bet would be to take any advice you find here with a grain of salt, and find your own path, which you will need to do anyway if you're going to survive in this industry. ;-)

Get set up with a brokerage which has a good paper-trading interface (one identical to their live interface). Stay away from the web-only interfaces.

Don't believe anything the broker's interface tells you about greeks. Assume everything is wrong (you'll find much of it is). Do your own work, write your own code.

Paper trade your code, starting with plain vanilla options.

Assume that much of what you find in books and papers is wrong as well (you still need to know it, if only for reference in conversations with others, and to know what you need to improve upon).

Continue past the first and second order derivatives quickly -- don't waste your time trying to over-optimize for those. Things start getting more interesting as you go up the scale, and as you get out of vanillas and into exotics.

Finally, once you think you're doing well on paper, open a real account, and prepare to be impressed with how quickly you're able to destroy capital -- you will. It's tuition cost, and you really don't start learning until your own money is on the line. Whether you actually take this step or not will have a lot to do with what sort of manager will hire you -- whether they want academic versus real-world skillset (there are advantages to both).

The other answers are useful and sensible. I have worked full time in equity research for nearly two decades, so very much a "qualitative" rather than a quantitative approach. However, all the firms for which I have worked had quants and because of my casual interest in the area I've spent a lot of time talking to quant teams over the years, often over a beer or two. Thinking back to those conversations, two things stand out.

Go where the money is. I mean that both in terms of what is popular at the moment (quant seems to have fashions like everything else) and also geographically if you can. Sure, quant can be done anywhere in theory but there will be places where there is more of it than in other locations. If you're working in a location with little demand and on techniques that are not in vogue, you will probably be paid less than others in the "right" place and pushing the "right" techniques.

Evolve. You're just trying to get in to the business, so it will be tempting - if you succeed - to think "Made it!" Actually, that's just the beginning. Whatever you do, assume it has a limited shelf-life and that you will have to continuously pick up new skills. Even on my side of the street, the changes over the past 10 years have been very significant and quantitative trading is developing far more rapidly. So cultivate and maintain an attitude of mental fluidity.

For your special background in mathematics see this excerpt from section 9:

The main challenge for a pure mathematician is to be able to get one’s
hands dirty and learning to be more focussed on getting numeric
results than on fancy theories. The main way to do this is to
implement pricing models for practice. If this doesn’t appeal you
aren’t suited to being a quant. There are quite a few ex-pure
mathematicians working in the city so it can certainly be done but
there is some prejudice in favour of applied maths and physics people.
Generally, people tend to hire people who are like them so if you can
ﬁnd anyone with a similar background working in the city, apply to
them.

I sometimes get asked by people whether they should do a pure maths
PhD or a ﬁnancial maths one. If you are absolutely sure you want to do
derivatives pricing then you should do it in ﬁnancial maths. (Yes, I
am taking PhD students but have no capacity at the moment.) If you
aren’t sure then don’t. A good compromise is to do stochastic
calculus, this is a hard area which will give plenty of intellectual
stimulation and leave you very well placed for working in derivatives
if you ever want to make the switch.